For continuous revolution coordinate r, selected signed lead schedule L(r) = L₀ + Kr integrates to signed axial position Z(r) = L₀r + Kr²/2. A schedule that crosses L = 0 stops and reverses axial feed; it is not a monotonic variable-lead thread.
Signed Linear-Lead Screw-Cutting Schedule
Explore a signed continuous linear-lead schedule and its integrated axial displacement and feed.
Equation Used
- Lead varies continuously and linearly with revolution coordinate.
- Spindle speed is constant.
- Lead and feed are signed axial quantities.
- Tool geometry, cutting loads, acceleration, control error, backlash and machine limits are excluded.
Z Travel is signed endpoint displacement, not necessarily monotonic cut length.
Spindle-synchronized signed feed reference
The animation ties spindle phase to the selected revolution coordinate and places the guided tool carriage at the integrated Z(r) position. The schedule plot shows lead versus revolution.
Negative lead denotes axial motion in the opposite direction. A zero crossing is displayed as a reversal, not silently clipped.
What the calculator determines
Select starting signed lead Lâ‚€, signed lead slope K, revolution span n and constant spindle speed N. Outputs are final signed lead, signed Z displacement, start feed and end feed.
No tool path code, acceleration limit, control following error, cutting force, thread form, depth schedule or machine capability is calculated.
Continuous signed schedule
L(r) = dZ/dr = L₀ + Kr and Z(r) = ∫₀ʳL(u)du = L₀r + Kr²/2. Feed in mm/min is NL(r). Units of K are mm/rev².
Selected-input arithmetic
For L₀ = 4 mm/rev, K = −0.05 mm/rev², n = 60 rev and N = 800 rpm, final signed lead is 1 mm/rev, signed Z displacement is 150 mm, start feed is 3,200 mm/min and end feed is 800 mm/min.
Scope and design boundary
This is schedule arithmetic, not a machining recommendation. If L(r) crosses zero within the selected span, Z(r) is non-monotonic and the same axial region may be revisited.
Unsupported machine brands, G-code compatibility, tolerances, servo limits, thermal diagnostics, applications and process advice are removed.
Questions
Why is K in mm/rev²?
It is the change in signed lead per revolution.
Can final lead be negative?
Yes mathematically; it means the scheduled axial direction has reversed.
Is axial length always a physical cut length?
No. It is signed endpoint displacement, especially when the schedule reverses.
Can this generate machine code?
No.
Speed and position checks for Screw-cutting Variable Pitch Mechanism
When screw-cutting variable pitch mechanism is automated with a linear actuator, check the required extension time at load rather than relying only on no-load speed. Load, force rating, and gearing all influence the final motion.
For press, clamp, or fixture motion, verify the actuator cannot overload tooling or create an unguarded pinch point. The control circuit should define the safe state after a jam or power loss.
Limit switches, controller timing, and mechanical hard stops should be reviewed together. A control scheme that works with one actuator family may behave differently if stroke, speed, or feedback type changes.
- Use loaded speed, not only no-load speed, when timing the motion.
- Confirm voltage, controller rating, and limit-switch behavior before wiring.
- Use feedback when synchronized or repeatable position control is required.
For FIRGELLI actuator control, use the linear actuator wiring diagram generator before wiring the final circuit and compare suitable actuator families in the FIRGELLI linear actuator range. If the machine already has an actuator, the linear actuator replacement finder can help shortlist replacements.
References & Further Reading
- Wikipedia contributors. Threading (manufacturing). Wikipedia
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
